If we simplify that equation, we can find a1. To write the explicit or closed form of a geometric sequence, we use anis the nth term of the sequence. So 3 must be raised to the power as a separate operation from the multiplication.

What is your answer? If we do not already have an explicit form, we must find it first before finding any term in a sequence. Now we use the formula to get Notice that writing an explicit formula always requires knowing the first term and the common ratio.

Find a6, a9, and a12 for problem 4. However, we have enough information to find it. The first time we used the formula, we were working backwards from an answer and the second time we were working forward to come up with the explicit formula.

Given the sequence 2, 6, 18, 54. Notice this example required making use of the general formula twice to get what we need. Find a6, a9, and a12 for problem 6. Rather than write a recursive formula, we can write an explicit formula.

Your formulas should be simplified if possible, but be very careful when working with exponential expressions. The explicit formula is also sometimes called the closed form. Find the explicit formula for 5, 10, 20, 40. In this situation, we have the first term, but do not know the common ratio.

If you need to review these topics, click here. What happens if we know a particular term and the common ratio, but not the entire sequence?

Now that we know the first term along with the r value given in the problem, we can find the explicit formula. But if you want to find the 12th term, then n does take on a value and it would be You will either be given this value or be given enough information to compute it.

The first term in the sequence is 2 and the common ratio is 3. Since we already found that in our first example, we can use it here. This is enough information to write the explicit formula.

So the explicit or closed formula for the geometric sequence is. The formula says that we need to know the first term and the common ratio. In this lesson, it is assumed that you know what an arithmetic sequence is and can find a common difference.

However, we do know two consecutive terms which means we can find the common ratio by dividing. This will give us Notice how much easier it is to work with the explicit formula than with the recursive formula to find a particular term in a sequence.

Using the recursive formula, we would have to know the first 49 terms in order to find the 50th.

Look at the example below to see what happens. If neither of those are given in the problem, you must take the given information and find them.

Site Navigation Geometric Sequences This lesson will work with arithmetic sequences, their recursive and explicit formulas and finding terms in a sequence. However, the recursive formula can become difficult to work with if we want to find the 50th term.

Find the recursive formula for 0. You must substitute a value for r into the formula. Find a6, a9, and a12 for problem 8. For example, when writing the general explicit formula, n is the variable and does not take on a value.

When writing the general expression for a geometric sequence, you will not actually find a value for this. DO NOT multiply the 2 and the 3 together.

To find the 10th term of any sequence, we would need to have an explicit formula for the sequence.Use the formula for the sum of a geometric series to determine the sum when a 1 =4 and r=2 and we have 12 terms. Using Explicit Formulas for Geometric Sequences Because a geometric sequence is an exponential function whose domain is the set of positive integers, and the common ratio is the base of the function, we can write explicit formulas that allow us to find particular terms.

Each number in the sequence is called a term (or sometimes "element" or "member"), read Sequences and Series for more details.

Arithmetic Sequence In an Arithmetic Sequence the difference between one term and the next is a constant. Geometric sequences calculator that shows all the work, detailed explanation and steps.

Site map; Math Tests; Geometric sequence is a list of numbers where each term is obtained by multiplying the previous term by a constant. probably have some question write me using the contact form or email me on Send Me A Comment. Comment: Email.

Given the sequence: {1, 4, 9, 16, } a) Write an explicit formula for this sequence. b) Write a recursive formula for this sequence. a n is the nth term of the sequence. When writing the general expression for a geometric sequence, you will not actually find a value for this.

It will be part of your formula much in the same way x’s and y’s are part of algebraic equations.

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